Objectif: Reply to Michael's question concerning the determination of
kinematic parameters from noisy landmarkers,

Dear Michael and to those who are concerned,

If I understand your question, you want to determine the rotation matrix R
and the translation vector V from noisy landmarker measurements. This is a
difficult problem.

Two main errors are involved: incertainty in determinationof tha landmark
coordinates by your opto-electrical system and error due to relative skin
movement. Generally, an opto-electrical system now can give a very acurate
measurement if the system is correctly calibrated and the cameras are
carefully positionned. Skin movement in some case is the most important
source of errors.

The bone movement itself can be considered as a rigid-body movement, which
can be described by R and V. But due to measurement errors, the bone movement
is no more a rigid-body movement. If you suppose that all measurement errors
are independent and normally distributed with constant standard deviation,
Veldpaus et al (1988) [A least square algorithm transfromation from spatial
marker coordinates, J. Biomch, 21, 45-54] proposed a very efficient algorithme
for the calculation of R. With my colleagues, we proposed also an algorithme
[WANG et al (1993), Using the polar decomposition theory to determine the
rotation matrix from noisy landmark measurements in the study of human joint
kinematics, 2nd Int Sym. of 3D analysis of human movement, Poitier,
July,France]. The advantage of our method is that it can theoretically seperate
the rotation from an orthotropic deformation. It provides also a tool to
quantify the deformation caused by measurement errors. But application of our
method needs a deep understanding of deformation nature, especially due to skin
movement. I don't think the skin movement can be simplified as a random
measurement error. Of cause, If the deformation nature is not known,
the algorithme proposed by Veldpaus is better, because it provides a solution
in a least-square sense.

>From this reply, I want to know if there exists a group who works on
this specific question (skin movement). If yes, I would like to know who
work in this group. If not, why we don't create such a group to share

Xuguang WANG, PhD